matlab introductory chapter, some basic usage remember about ~
M language is an interpreted language
the WHO : View the current variable
whoes : View the current variables and their dimension, such as the number of occupied bytes.
the Clear : Clear all variables
clear + variable name : Clear the variable
save save the current variable data to the default file name of the mat (.mat file A data file)
** save [** filename] [variable name] [variable name] [- append] [- ascii]
type of data
Numeric : double-precision, single-precision integer
a = 1; default established double data type
b = uint8 (a); b is converted to uint8;
a = uint8 (a); a is converted to uint8.
String
And character strings are used in single quotes , obtain ascii code value, or with double function abs
如double('a');
ascii characters into output
char function: char (63); ascii code 63 representative of the output character.
The string to a single quotation mark
str2num, num2str, eval ( 't = 1'): The statement is executed as string
Structure
Structures. Member Name = // expression could have been no need to declare the establishment of ...
isstruct: whether the structure. fieldnames, isfield function, rmfield function, getfield function
Unit
{} Using established: a = {1, 'str', [11 12 13 14]};
Multidimensional matrix
Matrix establish :
Direct Input: Peer elements or spaces separated by commas, semicolons different row elements used as the spacer
The establishment of 0,1 matrix: zeros (row, column); empathy established ones (row, column);
Colon expression vector established: e1: e2: e3 e1 which is an initial value, e2 in steps, e3 is the end value
Similar colon expression: linspace (sta, end, step_length);
Simple matrix :
Matrix Index: A (i, j) == A (i * (m-1) + j);
int / pair <int, int> find (A == 2): find elements in the matrix A is 2, returns the serial number or the coordinate, a plurality of answers to a plurality of return time.
ind2sub(size(A),ind); sub2ind(sizeof(A),x,y);
Rearrangement matrix: res = reshape (A, 9,1) <==> A (:);
Transposed matrix: A ';
Split (exception index matrix) matrix: M = A (1,:) <==> M = A: contents of a first row of all columns (1,1 end), and if M = A (1,1 : 3); line one to three
Remove the matrix elements: A (ind) = []; A (1, :) = [];
Matrix extension (replication): M = repmat (A, 2,1); (2 extend into the A matrix row one, as a whole wherein the element A)
Compression matrix (de-emphasis): A = [1 2 3 4 4]; S = unique (A);
Matrix processing base
The establishment of a special matrix
Matrix : I = eye (m, n ); General (m == n) (Well matrix (* ^ _ ^ *));
Random matrix : rand: randomly generating a uniform array of 0-1. randn: generating a random number between 0 and 1, normal distribution
e.g.: Sn = rand(1,10); Sn = randn(1,10);
Sn = a + (b - a) * rand (row, column); a ~ b uniformly random matrix
y = u + sqrt (s) * randn: generating random matrix mean u, s is the variance of the normal distribution
Mean mean function can be obtained sequence, std variance sequence can be obtained
Cube matrix : magic (5);
In Hilbert : Hilb (. 4) (the format RAT) may be output in the form of a rational number (H (i, j) = (i + j-1) / (i + j))
Toeplitz: toeplitz(1:6);
Matrix and vector operations
matlab as a unit matrix, the matrix may be directly implemented addition, multiplication and other operations matrix determinant, rank of the matrix, inverse matrix calculation and the like transpose
DET (A) : the determinant of the matrix A, if the determinant is not zero, then reversible.
INV (A) : the inverse matrix
Complex vector : a = [1 + 5i, 2,3 + 6i];
Vector inner product :. S = a * b ' (a, b are row vectors)
Linear Equations
A = [1,2,3;1,4,8;1,8,27];
b = [5,-2,6]’;
x = inv(A)*b; OR x = A/ b;
Simplification and similar matrix decomposition
Jordan Standard : jordan (A); [v J] = jordan (A); wherein V is a similarity transformation matrix, J is about canonical form
Eigenvalues : eig (A); [VJ ] = eig (A)
Matrix and vector norm
Norm : (A, 1) norm: 1 norm, norm (A, 2): 2 -norm, norm (A, inf): infinite norm, norm (A, 'fro' ): f norm
Matrix Analysis
Calculation function matrix derivative (number of elements in each derivative calculation function matrix) : the diff (A): find the first derivative. diff (A, 2) the second derivative.
Matrix function : funm (A, @ exp // @sin // @ cos);
Matlab program control structure
M文件：Script File、Function File.
Input data : input function. Data: disp function. Program pause: pause function (in seconds).
Branch and loop help for, help switch, help while , help if
Matlab dimensional high-level drawing operations
%%二维高层绘图
%基本绘图
x = 0:0.1:2*pi;
y = sin(x);
plot(x,y);
%第二个参数为矩阵
y1 = sin(x);
y2 = cos(x);
y3 = 0.002*exp(x);
y4 = x;
y5 = 0.002*tan(x);
z = [y1;y2;y3;y4;y5];
% plot(x,z);
%两个参数都是矩阵
x1 = 0:0.01:2*pi;
x2 = -pi:0.01:pi;
x = [x1;x2];
```
y1 = cos(x1);
y2 = sin(x2);
y = [y1;y2];
plot(x,y); % 按列绘图
plot(x',y');
% plot只有一个参数
x = linspace(0,2*pi,200);
y = sin(x);
plot(y)
y2 = cos(x);
y3 = y + i*y2;
plot(y3)
% plot有多个参数
x1 = linspace(0,2*pi,200);
x2 = linspace(0,2*pi,100);
y1 = cos(x1);
y2 = sin(x2);
plot(x1,y1,x2,y2)
% plot含有的曲线选项
x = linspace(0,2*pi,100);
y = sin(x);
plot(x,y,'r') %r g y m k b
plot(x,y,'*') % * . p < >
plot(x,y,':') %'--' '-' '-.' ':'
plot(x,y,'r*:')
```
%% 图形标注
x = linspace(0,2*pi,100);
y = sin(x);
plot(x,y);
xlabel('x');
ylabel('y');
title('正弦');
text(2,0.3,'y=sin(x)')
```
x1 = linspace(0,2*pi,200);
x2 = linspace(0,2*pi,100);
y1 = cos(x1);
y2 = sin(x2);
plot(x1,y1,x2,y2)
xlabel('x');
ylabel('y');
title('正弦');
text(2,0.3,'y=sin(x)^2');
text(0.5,0.2,'y=cos(x)_2');
legend('cos','sin');
%坐标轴控制
xlim([0 10])
% axis equal
```
%% 图像保持
x =0:0.1:2*pi;
y1 = sin(x);
y2 = cos(x);
hold on % 图形保持
plot(x,y1,'r');
plot(x,y2,'g');
hold off % 图形保持取消
%% 窗口分割
x = 0:0.1:2*pi;
y1 = sin(x);
y2 = cos(x);
y3 = tan(x);
y4 = exp(x);
subplot(221); % 将窗口分成2*2的小格,然后绘制第一个
plot(x,y1);
subplot(222);
plot(x,y2);
subplot(223);
plot(x,y3);
subplot(224);
plot(x,y4);Matlab symbolic operations
%符号变量
a = sym('a')
syms b;
b
%符号常量
c = sym('3');
%符号表达式
syms x
f1 = 3*x+6
f2 = 3*x+6
%符号四则运算
fadd1 = f1 + f2
fsub1 = f1 - f2
fmu1 = f1*f2
fdiv = f1 / f2
%符号表达式化简
syms x y
s = (x^2+y^2)^2+(x^2-y^2)^2;
spy = simplify(s);
%符号表达式和数值的转换
eval(c)
%因式分解，展开和合并同类项
syms a b x y
f1 = a^3 - b^3;
factor(f1) %因式分解
f2=(3*x^2+8*y^2)*(-x^2+3*y);
expand(f2) % 展开
f3=3*x^2+4*x^2+5*x^2*y;
collect(f3) % 合并同类型
%符号矩阵
a1 = [x x+y;y y^2]
transpose(a1) % 普通转置
a1' % 共轭转置
%符号函数值的求解
syms x
f1 = x^3-9;
subs(f1,3)
% 符号极限，符号微分，符号积分
syms x a
y =sin(x+a);
limit(y,0)
y2 = sqrt(1+exp(x));
diff(y2) % 数值中是求差分，符号计算是求解导数
diff(y2,2) % 求二重导数
diff(y2,3)
y3 = (3-x^2)^3; % 不定积分
int(y3)
% 求定积分
y4 = abs(1-x);
int(y4,1,2)
% 符号级数求和、泰勒级数
syms n
f = 1/ n^2;
s1 = symsum(f,n,1,inf) % 无穷级数
%泰勒展开
syms x
y = (1 + x + x^2) / (1 - x + x^2);
taylor(y,x,1,'Order',3) % 在x=1处进行taylor展开并且 得到第三项的值
%符号代数方程
clear
syms x
eval(solve(x+x*exp(x)-10))
% 方程组
clear
syms x y
[x y] = solve('x+y-98','x^(1/3)+y^(1/3)-2','x,y')
[x y] = solve('1/x^3+1/y^3-28','1/x+1/y-4','x,y')
%符号微分方程
dsolve('Dy-(x^2+y^2)/x^2/2','y(1)=2','x')